Stability of Jensen type mixed A1 - C3 functional equation in non-Archimedean (n, β) normed spaces

K. D. Sankar, S. Sampath

In this paper, we study the Hyers–Ulam stability of a newly introduced mixed-type functional equation that combines additive, cubic, and Jensen-type behaviors. The equation is investigated in the framework of non-Archimedean (n, β)-normed spaces, which provide a natural setting for extending classical stability theory to ultrametric environments. Using the direct method, we establish general stability results and obtain explicit bounds that measure the deviation of approximate solutions from exact ones. This approach unifies and extends several existing stability results related to Jensen-type, additive, and cubic functional equations. Our results contribute to the growing body of research on functional equations within non-Archimedean analysis and offer further insight into the structure of mixed-type equations in ultrametric spaces. 

Advanced Studies: Euro-Tbilisi Mathematical Journal, Vol. 19(2) (2026), pp. 87-97